Willmore-Chen tubes on homogeneous spaces in warped product spaces
type: Item
instance of: scholarly article
title: Willmore-Chen tubes on homogeneous spaces in warped product spaces
zbMATH Open document ID: 0921.53020
author: Manuel Barros
author: Josu Arroyo
author: Oscar J. Garay
published in: Pacific Journal of Mathematics
publication date: 1998-08-10T00:00:00Z
review text: We present a new method to obtain Willmore-Chen submanifolds in spaces endowed with warped product metrics and fibers being a given homogeneous space. The main points are: first, the invariance of the variational problem of Willmore-Chen with respect to the conformal changes in the ambient space metric; second, the principle of symmetric criticality which allows us to relate the problem with that for generalized elastic curves in the conformal structure on the base. We obtain some applications of our method, including one to get a rational one parameter family of Willmore tori in the standard 3-sphere shaped on an associated family of closed free elastic curves in the standard hyperbolic 2-plane. We also get a 3-dimensional Riemannian manifold which is foliated with leaves being nontrivial Willmore tori.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1186468
zbMATH Keywords: Willmore surface
zbMATH Keywords: elastic curve
zbMATH Keywords: conformal invariant
zbMATH Keywords: warped product
MaRDI profile type: Publication
full work available at URL: pjm.1999.188.201
OpenAlex ID: W2036504756
DOI: 10.2140/PJM.1999.188.201
description: scientific article; zbMATH DE number 1186468